I bought a brand new Specialized Hotrock 12 Coaster bike yesterday only to discover that the coaster brake ceases up after being applied when I got home. The crankshaft freezes up and will randomly unlock when fiddled with. I hope that makes sense.

Since the bike shop is so far away, I was wondering if anyone could give me a quick fix for this kind of issue before I pay a local bike shop to fix my brand new bike. I would really appreciate it.

Take it back. A new bike is supposed to work, and that is the main reason to purchase a new bike from a shop - they will fix things for some period of time at no additional charge. That service is built into the purchase price.

Try the following link for a complete description of a standard child's coaster brake and how to disassemble, overhaul, and reassemble it. There are pictures, but you probably need to play around with the parts yourself first before reading the description or else it will make less sense (for example, the "cone" part is not shaped like a cone at all):

It worked like a charm for my new bike that was seizing up, although I did nothing but wipe old grease off and repack the bearings. I thought perhaps the mechanism was put together incorrectly, so I did not pay attention when disassembling it and this guide proved very useful in figuring out how to put it back together.